But Batman as conceived by Bruce in BB was a symbol to inspire ALL the people of Gotham. His purpose wasn't to gain the trust of the police but inspire everyone in Gotham.

Nolan quite clearly sets the film up to where the next generation of Gotham is the one that will fight for it. Look how the orphans play such a role in the film. Some are going to help bring Bane's revolution ("They say there's work in the sewers.", the dead boy in the outlet) while others are still waiting for Batman's return ("You think he's coming back?"). Blake is an orphan already inspired by Batman as well as the events leading up to Batman's death. He's the only main character not in the know that Bruce Wayne is still alive. And he's also the one character that Bruce gives access to his cave so that he might go on in his stead.

Look at the faces of the kids in the bus and tell me that they aren't going to go on and help Gotham become a greater city past the film's events.